An intuitive way to explain the Monty hall problem

for the uninitiated heres a recap

when a mathematician 1st presented this problem on a talk show in 1990 she was met with a lot criticism and hate mail not just from common people of which only 8 % believed her result but from other mathematicians also of which only 35% believed … i dont know about you but even when it was explained to me i couldn’t rationally accept it so a few months back i thought of a new way to phrase the monty hall problem that makes it much more intuitive … heres the new problem : -
You have 100 doors only 1 of which has a car behind it , the host asks you to pick 1 then he discards 98 doors with goats behind them and asks if you want to switch to the only other door left… do you switch
i dont know why i haven’t seen anybody explain it like that it just makes so much more sense … its been bugging me for months thought i’d get it off my chest


explain how is this relevent

Its in offtopic section so it doesn’t have to relevant


its pretty relevant if you want to win a brand new car :tada:


But goats are so cool!

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I hope goat pictures don’t invade the forums… :goat:

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I wonder If we could some specs blind like this for the next project.

There are 100 screens. 99 of them are with light bleed 1 is without :))


i think this belongs here

The answer is that you should always switch, right? I saw a really good breakdown of the maths a while ago. The original is 3 doors, 2 with goats, 1 with the car. After picking the first one without opening, another door is opened and revealed to have a goat. The door you first chose has a 1/3 chance the car is behind it, so therefore between the other 2 doors there is a 2/3 chance of a car. Since the result of one of those doors has already been revealed, the 2/3 chance is entirely in the door you can switch to, so you should switch to it.


yes thats correct but that wasn’t the point of the post :sweat_smile: its still counter intuitive even when explained like that as i pointed out even mathematicians didn’t agree with the result initially

Does this result of always switching doors hold up in actuality though? I get why the math theory makes sense, but say this happened in real life. If the person switched doors a thousand times and kept their door another thousand times, I don’t think there would be a significant difference in the percentage of times you won the car instead of the goat.


ya the woman who presented it was having a very hard time convincing everybody so she told everybody to go out and do it practically … if you read my version i don’t think you would be suspicious about a difference in the math and the practical result

Great, entertainment and education.


However I wouldn’t have been too worried if I got the goat.
Because, afterall goat curry is one of my most favourite food dishes in the world.


I found this video put it really nicely


Isn’t this what Deal or No Deal essentially plays on? So if you get all the way to the end and there’s a jackpot plus one other out there, then you should switch boxes?


@Kee oh ya great point i didn’t think of that, im not sure, it gets a little more complex in that situation … the bankers use the same formula to calculate what offer to make you i think… ill post if i think of a solution

So… do you switch? :smile: I really don’t think there’s a difference… All doors are equal, so now there’s 50% chance to find a car behind any of them…

You pick wrong at first: The presenter picks a goat door and you decide to switch.

You pick right at first: The presenter picks a goat door and you decide to switch.

They say 2/3 if you pick wrong and 1/3 if you pick right at first, but the presenter just eliminated a possibility… So why is it still counted in the equation?


i thought about it for a while and its not exactly the same as the monty hall problem and it doesnt make a difference if you switch ill post a full explanation if i can put it convincingly

the difference between the monty hall problem and deal or no deal is that in monty hall 2 of the options can be counted as equal like 2 doors with goats behind them thats why you have a 2/3 chance of picking a door with a goat in deal or no deal two values cant be combined like that but say you started with only 3 suitcases 2 of which have 1 dollar in them (they dont have to be exactly the same as long as they are relatively the same it works) and 1 has 1 million dollars (this one has to be relatively different) then switching when one of the smaller values is revealed would give you the advantage

edit :- with some more thinking im not so sure about my logic so dont quote me… im pretty bad at probability that’s why i came up with the easy heuristic to understand the monty hall problem in the 1st place